Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions

Nicolas Champagnat 1, * Sylvie Roelly 2
* Auteur correspondant
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process|the conditioned multitype Feller branching diffusion are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too.
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Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2008, 13 (25), pp.777-810
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Nicolas Champagnat, Sylvie Roelly. Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2008, 13 (25), pp.777-810. 〈inria-00164758v2〉

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